The Mathematical Universe

Dedication

Acknowledgements

About the Author

Prologue

Preface

1. The Mystery of Mathematics

Let us be reasonable

All set

Where is Mathematics?

Fine tuning

A blast from the past: Euclid's geometry

Taking the Fifth further

Pi in the sky

Off to Monte Carlo

Smashed pi

The divine Isoperimetric Inequality

2. From Here to Infinity

Zeno's Paradox

Summing Up

In what Universe is this true?

The power of e

Fast money

What is normal?

3. Imaginary Worlds

The God-like Euler identity

Even more imaginaries - quaternions

But wait, there is more - octonians

The world's hardest problem - the Riemann Hypothesis

4. Random Universe

Going steady

Brownian Motion

Life is a gamble

The dating game

Information entropy

5. Order from Chaos

Cellular Automata

Life as a game

Infectious disease model - SIR

Mimicking Darwin

The whole is greater than the sum of its parts

Bees and termites

. And ants

Bacteria count

A hive of Mathematics: Fibonacci

Dynamical systems

Messrs. Fatou, Julia and Mandelbrot

The fractal Universe

6. Mathematics in Space

Down to Earth

Heavens above

Light-years

The great recession

The Universe is flat

Measuring the invisible: Black holes

A galaxy far, far away

Miniature Universe

Quantum world

Infinite space

Qubits

That equation

What time is it anyway?

Matters of gravity

Time in motion

Radiation

Symmetry and groups

8. The Unknowable Universe

Gödel incompleteness

Halting problem

EMX

Where is it, Dr. Heisenberg?

Summing up

Appendix I: Being Reasonable

Appendix II: Hyperbolic Geometry and Minkowski Spacetime

Appendix III: The Uncountable Real Numbers

Appendix IV: c² = c: Square and Line have Same Cardinality

Appendix V: Geometric Series

Appendix VI: Cesàro Sums

Appendix VII: Rotating a Vector via a Quaternion

Appendix VIII: Quaternions q ² = -1

Appendix IX: Riemann Zeta Function

Appendix X: Random Walk Code

Appendix XI: Age of the Solar System

Appendix XII: Chelyabinsk Meteoroid

Appendix XIII: Logic Gates

Appendix XIV: Galaxy Distance via Cepheids

Appendix XV: Time Dilation

Appendix XVI: Expansion of the Universe

Bibliography

Index